We study the synchronization of oscillators in 2D lattices with nearest
neighbor coupling. The boundaries between synchronized domains are due to
the motion of vortices. Since the phase winds by {\$}2$\backslash $pi{\$}
around a vortex, it generates {\$}2$\backslash $pi{\$} phase slips between
oscillators across its path. Thus, the synchronization behavior of the
system can be viewed in terms of the production, movement, and annihilation
of vortex pairs. Although the Kuramoto model is nonlinear, we show how to
use the steady state solution of the linearized model to predict where the
vortices are produced and how they move. We also study vortex density as a
function of system size and coupling. This vortex approach may lead to an
analytical understanding of why the lower critical dimension for macroscopic
entrainment is 2.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.J13.11